Event-based cameras provide high temporal resolution, robustness to lighting conditions and low power consumption, but their sparse, temporal data require models that reason over time. In supervised settings, this is increasingly handled with recurrent architectures. In contrast, most self-supervised learning (SSL) methods still adapt non-recurrent RGB techniques, with masking-based objectives that favor spatial reconstruction over temporal understanding. We introduce SPICE: Self-supervised Predictive Coding on Events, an SSL framework tailored to event data that processes longer sequences recurrently and learns by predicting future latent representations rather than reconstructing masked inputs, promoting a more natural objective focyused on anticipating what comes next. SPICE further incorporates an event-specific contrastive loss only operating on active regions. SPICE pre-training improves downstream performance on semantic segmentation, depth estimation and optical flow estimation. Low-dimensional projections confirm that the learned representations are meaningful and avoid collapse, while also revealing limitations in temporal stability and semantic organization, indicating clear directions for future event-specific SSL research. Code is available upon request.